A381385 E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)) / A(x) )^2.

1, 2, 6, 22, 64, -398, -14768, -288458, -4695168, -62117470, -385004032, 15463485398, 923640068096, 33487329741842, 957927747201024, 20185023268062070, 95909717192212480, -21197461265149558718, -1619210077600334151680, -82170388240550451506282, -3226620083793471277105152

Offset: 0

Author

Seiichi Manyama, Feb 22 2025

Keywords

• sign

Crossrefs

Cf. A136630, A381384.

Programs

PARI

a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = 2*sum(k=0, n, k!*binomial(2*n-k+2, k)/(2*n-k+2)*I^(n-k)*a136630(n, k));

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381384.

a(n) = 2 * Sum_{k=0..n} k! * binomial(2*n-k+2,k)/(2*n-k+2) * i^(n-k) * A136630(n,k), where i is the imaginary unit.